Download Activity_4_6_3 - Connecticut Core Standards

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Activity 4.6.3 Applying Right Triangle Trigonometry
1. Over the vacation your uncle wanted to cut down a tree that was on his property. He did not
want the tree to hit his house when it came down. So he measured the distance from the base of
the tree to the base of the house. While he did not know how tall the tree was, he did know that
the angle of elevation from the ground at the base of the house to the top of the tree was 17 . Is
there enough room to cut the tree down without hitting the house. Why or why not?.
17
131 feet
2. Emily is a great swimmer and like any good swimmer she knows her limits. She wants to
swim across the Connecticut River from Wethersfield to Glastonbury and then back to
Wethersfield. Her friends tell her that it is too far. However, Emily is a great geometry student
and is going to find out herself if the swim is within her limits.
Emily places a stake in the ground that is directly across from a rock on the other side of the
river. Then she walks 175 feet down shore and places another stake. She then measures the
angle formed by the line on the beach and the line of sight to the rock to be 72 .
Rock
Wethersfield
175’
72
Glastonbury
a.
To the nearest foot, determine how wide the river is at the point of the rock.
b.
If Emily can swim up to a quarter mile without stopping, will she be able to make
this swim if she doesn’t take a break? Show all work.
c. If Emily decides to swim straight across the river what might prevent her from
arriving exactly at the rock?
Activity 4.6.3
Connecticut Core Geometry Curriculum Version 3.0
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3. A see-saw, 15 feet long, rests on a pivot at its midpoint 3 feet above the ground. Through
what maximum angle can the see-saw rotate? Round your solution to the nearest tenth of a
degree.
4. Captain Trig is flying his geometry class to a vacation resort where they will further develop
their geometry skills. To begin Captain Trig gives the class a problem before they even land. He
tells them that the plane is currently 22,000 feet in the air and the runway is 8 miles away from a
point directly below the plane. If they begin descending now, at what angle of descent should
they set the plane? Draw a diagram of this to help you and your crew and
round your solution to the nearest tenth of a degree.
5. A water-lily was growing 10 cm above the surface of a pond when a strong wind came and
blew it 50 cm sideways to the surface of the pond.
a. Use this information to determine the depth of the pond. Assume the stem is rigid and does
not bend.
10cm
b. To the nearest hundredth of a degree, through what angle measure
did the stem of the water-lily rotate from the wind?
Activity 4.6.3
50 cm
Connecticut Core Geometry Curriculum Version 3.0
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Date:
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6. Jamie is lying on the edge of the top of a building looking at a bird that is sitting on an
edge of the roof of another building below him. The building Jamie is on is 128 feet tall
and the building the bird is on is 72 feet tall. The buildings were built on the same
elevation and are 307 feet apart. Through what angle of depression is Jamie is viewing
the bird through his binoculars?
7. Use the diagram to answer these questions.
a. Can you use right triangle trigonometry to find
the missing angle measures in the diagram? Why or
why not?
b. If you answered “no” in part (a), then determine what type of triangle is shown
below. If you answered yes, then find each missing angle measure.
8. Due to increased texting in New Britain, the local cell phone company has put up a new
cell phone tower. You want to know the height of the tower. However, the area where
it is located is off limits for security reasons so you can’t find out how far you are away
from the tower. Instead, from a point outside the fenced area you get an angle of
elevation from a point to the top of the tower. Call this point A. The angle of elevation is
41.5 from point A to the top of the tower. Then you walk 72 feet closer to the tower and
measure the angle of elevation at point B to be 62 . To the nearest foot what is the
height of the tower? (Use the diagram below and solve for both x and h.)
Activity 4.6.3
Connecticut Core Geometry Curriculum Version 3.0